Pure-Hollow Modules and Pure-Lifting Modules

Khawla Ahmed; Nuhad S. Al. Mothafar

doi:10.24996/ijs.2024.65.3.32

Authors

Khawla Ahmed Department of Mathematics, College of Science, University of Baghdad, Iraq https://orcid.org/0009-0004-7107-8144
Nuhad S. Al. Mothafar Department of Mathematics, College of Science, University of Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2024.65.3.32

Keywords:

small submodule, hollow module, lifting module, Pure hollow, pure lifting

Abstract

Let be a commutative ring with identity, and be a unitary left R-module. In this paper we, introduce and study a new class of modules called pure hollow (Pr-hollow) and pure-lifting (Pr-lifting). We give a fundamental, properties of these concept. also, we, introduce some conditions under which the quotient and direct sum of Pr-lifting modules is Pr-lifting.